article

The Gröbner fan of an ideal

Authors:

Lorenzo RobbianoAuthors Info & Claims

Journal of Symbolic Computation, Volume 6, Issue 2-3

Pages 183 - 208

https://doi.org/10.1016/S0747-7171(88)80042-7

Published: 01 December 1988 Publication History

Abstract

To every ideal I in the polynomial ring A:=k[X"1,..., X"n] new invariants are attached, such as the Grobner Fan F(I), the Grobner region G(I) and the set ATO(I) of the almost term-orderings of I, i.e. orderings which ''behave like'' term-orderings with respect to I. These invariants arise by considering the reduced Grobner bases of I with respect to all the term-orderings. Moreover F(I), G(I), ATO(I) can be got in a constructive way, as we show by producing a suitable algorithm which computes them.

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Cited By

Vaccon TVerron T(2023)Universal Analytic Gröbner Bases and Tropical GeometryProceedings of the 2023 International Symposium on Symbolic and Algebraic Computation10.1145/3597066.3597110(517-525)Online publication date: 24-Jul-2023
https://dl.acm.org/doi/10.1145/3597066.3597110
Astrelin AGolubitsky OPankratiev E(2023)Involutive bases of ideals in the ring of polynomialsProgramming and Computing Software10.1007/BF0275917726:1(31-35)Online publication date: 15-Mar-2023
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The Gröbner fan of an ideal

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Published In

cover image Journal of Symbolic Computation

Journal of Symbolic Computation Volume 6, Issue 2-3

Oct./Dec. 1988

247 pages

ISSN:0747-7171

Editor:
Bruno Buchberger

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Copyright © Academic Press Limited © 1988.

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Academic Press, Inc.

United States

Publication History

Published: 01 December 1988

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Cited By

Vaccon TVerron T(2023)Universal Analytic Gröbner Bases and Tropical GeometryProceedings of the 2023 International Symposium on Symbolic and Algebraic Computation10.1145/3597066.3597110(517-525)Online publication date: 24-Jul-2023
https://dl.acm.org/doi/10.1145/3597066.3597110
Astrelin AGolubitsky OPankratiev E(2023)Involutive bases of ideals in the ring of polynomialsProgramming and Computing Software10.1007/BF0275917726:1(31-35)Online publication date: 15-Mar-2023
https://dl.acm.org/doi/10.1007/BF02759177
Caruso XVaccon TVerron TMaza MZhi L(2022)On Polynomial Ideals and Overconvergence in Tate AlgebrasProceedings of the 2022 International Symposium on Symbolic and Algebraic Computation10.1145/3476446.3535491(489-497)Online publication date: 4-Jul-2022
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Markwig TRen Y(2020)Computing Tropical Varieties Over Fields with ValuationFoundations of Computational Mathematics10.1007/s10208-019-09430-220:4(783-800)Online publication date: 1-Aug-2020
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Perry J(2020)A dynamic F4 algorithm to compute Gröbner basesApplicable Algebra in Engineering, Communication and Computing10.1007/s00200-020-00450-y31:5-6(411-434)Online publication date: 1-Nov-2020
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Perry JYap CEl Din M(2017)Exploring the Dynamic Buchberger AlgorithmProceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation10.1145/3087604.3087643(365-372)Online publication date: 23-Jul-2017
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Markwig TRen YWienand O(2017)Standard bases in mixed power series and polynomial rings over ringsJournal of Symbolic Computation10.1016/j.jsc.2016.08.00979:P1(119-139)Online publication date: 1-Mar-2017
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Maruri-Aguilar HSáenz-De-Cabezón EWynn H(2012)Betti numbers of polynomial hierarchical models for experimental designsAnnals of Mathematics and Artificial Intelligence10.1007/s10472-012-9295-964:4(411-426)Online publication date: 1-Apr-2012
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